The Sun says Johnson has been offered a double-your-money, five-year deal to stay at Manchester City.
Liverpool were among the clubs alerted when it was revealed the midfielder was unhappy with his current contract at City.
But Johnson, 20, is now being tempted by an agreement worth £25,000 a week until 2013.
Boss Mark Hughes said: "He's a young player with a great future and we want that to be at City.
"Everything is there for him to develop and I'm sure he will become a regular in the England side.
"He's an outstanding young talent and we fully expect him to be with us for many years."